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arXiv · 2603.05809

On an elementary method for solving $Ax^4-By^2=1$

P. G. Walsh
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Abstract

A new method for solving quartic equations due to Luo and Lin is investigated both computationally and theoretically. As a result, a completely straightforward elementary method is given for solving Bumby's equation $3X^4-2Y^2=1$, along with a conjecture, which if resolved, would enable a similar proof for a possibly infinite family of similar equations.

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P. G. Walsh. 2026-03-06. On an elementary method for solving $Ax^4-By^2=1$. https://doi.org/10.7169/facm%2F251013-23-12

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